Graduates promptly welded instrument (7)
I believe the answer is:
bassoon
'instrument' is the definition.
(bassoon is a kind of instrument)
'graduates promptly' is the wordplay.
'graduates' becomes 'BAs' (people with Bachelor of Arts degrees).
'promptly' becomes 'soon' (I've seen this in another clue).
'bas'+'soon'='BASSOON'
'welded' acts as a link.
I am not very happy about this link. It may belong to another bit of the clue.
Can you help me to learn more?
(Other definitions for bassoon that I've seen before include "Tenor of the oboe family" , "wind player" , "Instrument heard by Wedding-Guest" , "It is played" , "Hollow instrument" .)